If at least one root of 2x2+3x+5=0 and ax2+bx+c=0,a,b,c∈N  is common, then the maximum value of a+ b +c is

Roots of the equation 2x2+3x+5=0 arex=−3±9−406 (imaginary roots) Hence, both roots coincide, so on comparinga2=b3=c5=k ⇒        a=2k,b=3k,c=5k⇒        a+b+c=10kSo, maximum value does not exist.